12 Search Results for "Celis, L. Elisa"


Volume

LIPIcs, Volume 218

3rd Symposium on Foundations of Responsible Computing (FORC 2022)

FORC 2022, June 6-8, 2022, Cambridge, MA, USA

Editors: L. Elisa Celis

Document
Complete Volume
LIPIcs, Volume 218, FORC 2022, Complete Volume

Authors: L. Elisa Celis

Published in: LIPIcs, Volume 218, 3rd Symposium on Foundations of Responsible Computing (FORC 2022)


Abstract
LIPIcs, Volume 218, FORC 2022, Complete Volume

Cite as

3rd Symposium on Foundations of Responsible Computing (FORC 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 218, pp. 1-148, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)


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@Proceedings{celis:LIPIcs.FORC.2022,
  title =	{{LIPIcs, Volume 218, FORC 2022, Complete Volume}},
  booktitle =	{3rd Symposium on Foundations of Responsible Computing (FORC 2022)},
  pages =	{1--148},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-226-6},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{218},
  editor =	{Celis, L. Elisa},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FORC.2022},
  URN =		{urn:nbn:de:0030-drops-165222},
  doi =		{10.4230/LIPIcs.FORC.2022},
  annote =	{Keywords: LIPIcs, Volume 218, FORC 2022, Complete Volume}
}
Document
Front Matter
Front Matter, Table of Contents, Preface, Conference Organization

Authors: L. Elisa Celis

Published in: LIPIcs, Volume 218, 3rd Symposium on Foundations of Responsible Computing (FORC 2022)


Abstract
Front Matter, Table of Contents, Preface, Conference Organization

Cite as

3rd Symposium on Foundations of Responsible Computing (FORC 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 218, pp. 0:i-0:x, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)


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@InProceedings{celis:LIPIcs.FORC.2022.0,
  author =	{Celis, L. Elisa},
  title =	{{Front Matter, Table of Contents, Preface, Conference Organization}},
  booktitle =	{3rd Symposium on Foundations of Responsible Computing (FORC 2022)},
  pages =	{0:i--0:x},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-226-6},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{218},
  editor =	{Celis, L. Elisa},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FORC.2022.0},
  URN =		{urn:nbn:de:0030-drops-165230},
  doi =		{10.4230/LIPIcs.FORC.2022.0},
  annote =	{Keywords: Front Matter, Table of Contents, Preface, Conference Organization}
}
Document
Controlling Privacy Loss in Sampling Schemes: An Analysis of Stratified and Cluster Sampling

Authors: Mark Bun, Jörg Drechsler, Marco Gaboardi, Audra McMillan, and Jayshree Sarathy

Published in: LIPIcs, Volume 218, 3rd Symposium on Foundations of Responsible Computing (FORC 2022)


Abstract
Sampling schemes are fundamental tools in statistics, survey design, and algorithm design. A fundamental result in differential privacy is that a differentially private mechanism run on a simple random sample of a population provides stronger privacy guarantees than the same algorithm run on the entire population. However, in practice, sampling designs are often more complex than the simple, data-independent sampling schemes that are addressed in prior work. In this work, we extend the study of privacy amplification results to more complex, data-dependent sampling schemes. We find that not only do these sampling schemes often fail to amplify privacy, they can actually result in privacy degradation. We analyze the privacy implications of the pervasive cluster sampling and stratified sampling paradigms, as well as provide some insight into the study of more general sampling designs.

Cite as

Mark Bun, Jörg Drechsler, Marco Gaboardi, Audra McMillan, and Jayshree Sarathy. Controlling Privacy Loss in Sampling Schemes: An Analysis of Stratified and Cluster Sampling. In 3rd Symposium on Foundations of Responsible Computing (FORC 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 218, pp. 1:1-1:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)


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@InProceedings{bun_et_al:LIPIcs.FORC.2022.1,
  author =	{Bun, Mark and Drechsler, J\"{o}rg and Gaboardi, Marco and McMillan, Audra and Sarathy, Jayshree},
  title =	{{Controlling Privacy Loss in Sampling Schemes: An Analysis of Stratified and Cluster Sampling}},
  booktitle =	{3rd Symposium on Foundations of Responsible Computing (FORC 2022)},
  pages =	{1:1--1:24},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-226-6},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{218},
  editor =	{Celis, L. Elisa},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FORC.2022.1},
  URN =		{urn:nbn:de:0030-drops-165243},
  doi =		{10.4230/LIPIcs.FORC.2022.1},
  annote =	{Keywords: privacy, differential privacy, survey design, survey sampling}
}
Document
Leximax Approximations and Representative Cohort Selection

Authors: Monika Henzinger, Charlotte Peale, Omer Reingold, and Judy Hanwen Shen

Published in: LIPIcs, Volume 218, 3rd Symposium on Foundations of Responsible Computing (FORC 2022)


Abstract
Finding a representative cohort from a broad pool of candidates is a goal that arises in many contexts such as choosing governing committees and consumer panels. While there are many ways to define the degree to which a cohort represents a population, a very appealing solution concept is lexicographic maximality (leximax) which offers a natural (pareto-optimal like) interpretation that the utility of no population can be increased without decreasing the utility of a population that is already worse off. However, finding a leximax solution can be highly dependent on small variations in the utility of certain groups. In this work, we explore new notions of approximate leximax solutions with three distinct motivations: better algorithmic efficiency, exploiting significant utility improvements, and robustness to noise. Among other definitional contributions, we give a new notion of an approximate leximax that satisfies a similarly appealing semantic interpretation and relate it to algorithmically-feasible approximate leximax notions. When group utilities are linear over cohort candidates, we give an efficient polynomial-time algorithm for finding a leximax distribution over cohort candidates in the exact as well as in the approximate setting. Furthermore, we show that finding an integer solution to leximax cohort selection with linear utilities is NP-Hard.

Cite as

Monika Henzinger, Charlotte Peale, Omer Reingold, and Judy Hanwen Shen. Leximax Approximations and Representative Cohort Selection. In 3rd Symposium on Foundations of Responsible Computing (FORC 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 218, pp. 2:1-2:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)


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@InProceedings{henzinger_et_al:LIPIcs.FORC.2022.2,
  author =	{Henzinger, Monika and Peale, Charlotte and Reingold, Omer and Shen, Judy Hanwen},
  title =	{{Leximax Approximations and Representative Cohort Selection}},
  booktitle =	{3rd Symposium on Foundations of Responsible Computing (FORC 2022)},
  pages =	{2:1--2:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-226-6},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{218},
  editor =	{Celis, L. Elisa},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FORC.2022.2},
  URN =		{urn:nbn:de:0030-drops-165258},
  doi =		{10.4230/LIPIcs.FORC.2022.2},
  annote =	{Keywords: fairness, cohort selection, leximin, maxmin}
}
Document
On Classification of Strategic Agents Who Can Both Game and Improve

Authors: Saba Ahmadi, Hedyeh Beyhaghi, Avrim Blum, and Keziah Naggita

Published in: LIPIcs, Volume 218, 3rd Symposium on Foundations of Responsible Computing (FORC 2022)


Abstract
In this work, we consider classification of agents who can both game and improve. For example, people wishing to get a loan may be able to take some actions that increase their perceived credit-worthiness and others that also increase their true credit-worthiness. A decision-maker would like to define a classification rule with few false-positives (does not give out many bad loans) while yielding many true positives (giving out many good loans), which includes encouraging agents to improve to become true positives if possible. We consider two models for this problem, a general discrete model and a linear model, and prove algorithmic, learning, and hardness results for each. For the general discrete model, we give an efficient algorithm for the problem of maximizing the number of true positives subject to no false positives, and show how to extend this to a partial-information learning setting. We also show hardness for the problem of maximizing the number of true positives subject to a nonzero bound on the number of false positives, and that this hardness holds even for a finite-point version of our linear model. We also show that maximizing the number of true positives subject to no false positive is NP-hard in our full linear model. We additionally provide an algorithm that determines whether there exists a linear classifier that classifies all agents accurately and causes all improvable agents to become qualified, and give additional results for low-dimensional data.

Cite as

Saba Ahmadi, Hedyeh Beyhaghi, Avrim Blum, and Keziah Naggita. On Classification of Strategic Agents Who Can Both Game and Improve. In 3rd Symposium on Foundations of Responsible Computing (FORC 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 218, pp. 3:1-3:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)


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@InProceedings{ahmadi_et_al:LIPIcs.FORC.2022.3,
  author =	{Ahmadi, Saba and Beyhaghi, Hedyeh and Blum, Avrim and Naggita, Keziah},
  title =	{{On Classification of Strategic Agents Who Can Both Game and Improve}},
  booktitle =	{3rd Symposium on Foundations of Responsible Computing (FORC 2022)},
  pages =	{3:1--3:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-226-6},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{218},
  editor =	{Celis, L. Elisa},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FORC.2022.3},
  URN =		{urn:nbn:de:0030-drops-165269},
  doi =		{10.4230/LIPIcs.FORC.2022.3},
  annote =	{Keywords: Strategic Classification, Social Welfare, Learning}
}
Document
Individually-Fair Auctions for Multi-Slot Sponsored Search

Authors: Shuchi Chawla, Rojin Rezvan, and Nathaniel Sauerberg

Published in: LIPIcs, Volume 218, 3rd Symposium on Foundations of Responsible Computing (FORC 2022)


Abstract
We design fair sponsored search auctions that achieve a near-optimal tradeoff between fairness and quality. Our work builds upon the model and auction design of Chawla and Jagadeesan [Chawla and Jagadeesan, 2022], who considered the special case of a single slot. We consider sponsored search settings with multiple slots and the standard model of click through rates that are multiplicatively separable into an advertiser-specific component and a slot-specific component. When similar users have similar advertiser-specific click through rates, our auctions achieve the same near-optimal tradeoff between fairness and quality as in [Chawla and Jagadeesan, 2022]. When similar users can have different advertiser-specific preferences, we show that a preference-based fairness guarantee holds. Finally, we provide a computationally efficient algorithm for computing payments for our auctions as well as those in previous work, resolving another open direction from [Chawla and Jagadeesan, 2022].

Cite as

Shuchi Chawla, Rojin Rezvan, and Nathaniel Sauerberg. Individually-Fair Auctions for Multi-Slot Sponsored Search. In 3rd Symposium on Foundations of Responsible Computing (FORC 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 218, pp. 4:1-4:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)


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@InProceedings{chawla_et_al:LIPIcs.FORC.2022.4,
  author =	{Chawla, Shuchi and Rezvan, Rojin and Sauerberg, Nathaniel},
  title =	{{Individually-Fair Auctions for Multi-Slot Sponsored Search}},
  booktitle =	{3rd Symposium on Foundations of Responsible Computing (FORC 2022)},
  pages =	{4:1--4:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-226-6},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{218},
  editor =	{Celis, L. Elisa},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FORC.2022.4},
  URN =		{urn:nbn:de:0030-drops-165272},
  doi =		{10.4230/LIPIcs.FORC.2022.4},
  annote =	{Keywords: algorithmic fairness, advertising auctions, and individual fairness}
}
Document
Robustness Should Not Be at Odds with Accuracy

Authors: Sadia Chowdhury and Ruth Urner

Published in: LIPIcs, Volume 218, 3rd Symposium on Foundations of Responsible Computing (FORC 2022)


Abstract
The phenomenon of adversarial examples in deep learning models has caused substantial concern over their reliability and trustworthiness: in many instances an imperceptible perturbation can falsely flip a neural network’s prediction. Applied research in this area has mostly focused on developing novel adversarial attack strategies or building better defenses against such. It has repeatedly been pointed out that adversarial robustness may be in conflict with requirements for high accuracy. In this work, we take a more principled look at modeling the phenomenon of adversarial examples. We argue that deciding whether a model’s label change under a small perturbation is justified, should be done in compliance with the underlying data-generating process. Through a series of formal constructions, systematically analyzing the relation between standard Bayes classifiers and robust-Bayes classifiers, we make the case for adversarial robustness as a locally adaptive measure. We propose a novel way defining such a locally adaptive robust loss, show that it has a natural empirical counterpart, and develop resulting algorithmic guidance in form of data-informed adaptive robustness radius. We prove that our adaptive robust data-augmentation maintains consistency of 1-nearest neighbor classification under deterministic labels and thereby argue that robustness should not be at odds with accuracy.

Cite as

Sadia Chowdhury and Ruth Urner. Robustness Should Not Be at Odds with Accuracy. In 3rd Symposium on Foundations of Responsible Computing (FORC 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 218, pp. 5:1-5:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)


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@InProceedings{chowdhury_et_al:LIPIcs.FORC.2022.5,
  author =	{Chowdhury, Sadia and Urner, Ruth},
  title =	{{Robustness Should Not Be at Odds with Accuracy}},
  booktitle =	{3rd Symposium on Foundations of Responsible Computing (FORC 2022)},
  pages =	{5:1--5:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-226-6},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{218},
  editor =	{Celis, L. Elisa},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FORC.2022.5},
  URN =		{urn:nbn:de:0030-drops-165280},
  doi =		{10.4230/LIPIcs.FORC.2022.5},
  annote =	{Keywords: Statistical Learning Theory, Bayes optimal classifier, adversarial perturbations, adaptive robust loss}
}
Document
Improved Generalization Guarantees in Restricted Data Models

Authors: Elbert Du and Cynthia Dwork

Published in: LIPIcs, Volume 218, 3rd Symposium on Foundations of Responsible Computing (FORC 2022)


Abstract
Differential privacy is known to protect against threats to validity incurred due to adaptive, or exploratory, data analysis - even when the analyst adversarially searches for a statistical estimate that diverges from the true value of the quantity of interest on the underlying population. The cost of this protection is the accuracy loss incurred by differential privacy. In this work, inspired by standard models in the genomics literature, we consider data models in which individuals are represented by a sequence of attributes with the property that where distant attributes are only weakly correlated. We show that, under this assumption, it is possible to "re-use" privacy budget on different portions of the data, significantly improving accuracy without increasing the risk of overfitting.

Cite as

Elbert Du and Cynthia Dwork. Improved Generalization Guarantees in Restricted Data Models. In 3rd Symposium on Foundations of Responsible Computing (FORC 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 218, pp. 6:1-6:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)


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@InProceedings{du_et_al:LIPIcs.FORC.2022.6,
  author =	{Du, Elbert and Dwork, Cynthia},
  title =	{{Improved Generalization Guarantees in Restricted Data Models}},
  booktitle =	{3rd Symposium on Foundations of Responsible Computing (FORC 2022)},
  pages =	{6:1--6:12},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-226-6},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{218},
  editor =	{Celis, L. Elisa},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FORC.2022.6},
  URN =		{urn:nbn:de:0030-drops-165299},
  doi =		{10.4230/LIPIcs.FORC.2022.6},
  annote =	{Keywords: Differential Privacy, Adaptive Data Analysis, Transfer Theorem}
}
Document
Differential Secrecy for Distributed Data and Applications to Robust Differentially Secure Vector Summation

Authors: Kunal Talwar

Published in: LIPIcs, Volume 218, 3rd Symposium on Foundations of Responsible Computing (FORC 2022)


Abstract
Computing the noisy sum of real-valued vectors is an important primitive in differentially private learning and statistics. In private federated learning applications, these vectors are held by client devices, leading to a distributed summation problem. Standard Secure Multiparty Computation protocols for this problem are susceptible to poisoning attacks, where a client may have a large influence on the sum, without being detected. In this work, we propose a poisoning-robust private summation protocol in the multiple-server setting, recently studied in PRIO [Henry Corrigan-Gibbs and Dan Boneh, 2017]. We present a protocol for vector summation that verifies that the Euclidean norm of each contribution is approximately bounded. We show that by relaxing the security constraint in SMC to a differential privacy like guarantee, one can improve over PRIO in terms of communication requirements as well as the client-side computation. Unlike SMC algorithms that inevitably cast integers to elements of a large finite field, our algorithms work over integers/reals, which may allow for additional efficiencies.

Cite as

Kunal Talwar. Differential Secrecy for Distributed Data and Applications to Robust Differentially Secure Vector Summation. In 3rd Symposium on Foundations of Responsible Computing (FORC 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 218, pp. 7:1-7:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)


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@InProceedings{talwar:LIPIcs.FORC.2022.7,
  author =	{Talwar, Kunal},
  title =	{{Differential Secrecy for Distributed Data and Applications to Robust Differentially Secure Vector Summation}},
  booktitle =	{3rd Symposium on Foundations of Responsible Computing (FORC 2022)},
  pages =	{7:1--7:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-226-6},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{218},
  editor =	{Celis, L. Elisa},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FORC.2022.7},
  URN =		{urn:nbn:de:0030-drops-165302},
  doi =		{10.4230/LIPIcs.FORC.2022.7},
  annote =	{Keywords: Zero Knowledge, Secure Summation, Differential Privacy}
}
Document
Ranking with Fairness Constraints

Authors: L. Elisa Celis, Damian Straszak, and Nisheeth K. Vishnoi

Published in: LIPIcs, Volume 107, 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018)


Abstract
Ranking algorithms are deployed widely to order a set of items in applications such as search engines, news feeds, and recommendation systems. Recent studies, however, have shown that, left unchecked, the output of ranking algorithms can result in decreased diversity in the type of content presented, promote stereotypes, and polarize opinions. In order to address such issues, we study the following variant of the traditional ranking problem when, in addition, there are fairness or diversity constraints. Given a collection of items along with 1) the value of placing an item in a particular position in the ranking, 2) the collection of sensitive attributes (such as gender, race, political opinion) of each item and 3) a collection of fairness constraints that, for each k, bound the number of items with each attribute that are allowed to appear in the top k positions of the ranking, the goal is to output a ranking that maximizes the value with respect to the original rank quality metric while respecting the constraints. This problem encapsulates various well-studied problems related to bipartite and hypergraph matching as special cases and turns out to be hard to approximate even with simple constraints. Our main technical contributions are fast exact and approximation algorithms along with complementary hardness results that, together, come close to settling the approximability of this constrained ranking maximization problem. Unlike prior work on the approximability of constrained matching problems, our algorithm runs in linear time, even when the number of constraints is (polynomially) large, its approximation ratio does not depend on the number of constraints, and it produces solutions with small constraint violations. Our results rely on insights about the constrained matching problem when the objective function satisfies certain properties that appear in common ranking metrics such as discounted cumulative gain (DCG), Spearman's rho or Bradley-Terry, along with the nested structure of fairness constraints.

Cite as

L. Elisa Celis, Damian Straszak, and Nisheeth K. Vishnoi. Ranking with Fairness Constraints. In 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 107, pp. 28:1-28:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)


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@InProceedings{celis_et_al:LIPIcs.ICALP.2018.28,
  author =	{Celis, L. Elisa and Straszak, Damian and Vishnoi, Nisheeth K.},
  title =	{{Ranking with Fairness Constraints}},
  booktitle =	{45th International Colloquium on Automata, Languages, and Programming (ICALP 2018)},
  pages =	{28:1--28:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-076-7},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{107},
  editor =	{Chatzigiannakis, Ioannis and Kaklamanis, Christos and Marx, D\'{a}niel and Sannella, Donald},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2018.28},
  URN =		{urn:nbn:de:0030-drops-90329},
  doi =		{10.4230/LIPIcs.ICALP.2018.28},
  annote =	{Keywords: Ranking, Fairness, Optimization, Matching, Approximation Algorithms}
}
Document
On the Complexity of Constrained Determinantal Point Processes

Authors: L. Elisa Celis, Amit Deshpande, Tarun Kathuria, Damian Straszak, and Nisheeth K. Vishnoi

Published in: LIPIcs, Volume 81, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2017)


Abstract
Determinantal Point Processes (DPPs) are probabilistic models that arise in quantum physics and random matrix theory and have recently found numerous applications in theoretical computer science and machine learning. DPPs define probability distributions over subsets of a given ground set, they exhibit interesting properties such as negative correlation, and, unlike other models of negative correlation such as Markov random fields, have efficient algorithms for sampling. When applied to kernel methods in machine learning, DPPs favor subsets of the given data with more diverse features. However, many real-world applications require efficient algorithms to sample from DPPs with additional constraints on the sampled subset, e.g., partition or matroid constraints that are important from the viewpoint of ensuring priors, resource or fairness constraints on the sampled subset. Whether one can efficiently sample from DPPs in such constrained settings is an important problem that was first raised in a survey of DPPs for machine learning by Kulesza and Taskar and studied in some recent works. The main contribution of this paper is the first resolution of the complexity of sampling from DPPs with constraints. On the one hand, we give exact efficient algorithms for sampling from constrained DPPs when the description of the constraints is in unary; this includes special cases of practical importance such as a small number of partition, knapsack or budget constraints. On the other hand, we prove that when the constraints are specified in binary, this problem is #P-hard via a reduction from the problem of computing mixed discriminants; implying that it may be unlikely that there is an FPRAS. Technically, our algorithmic result benefits from viewing the constrained sampling problem via the lens of polynomials and we obtain our complexity results by providing an equivalence between computing mixed discriminants and sampling from partition constrained DPPs. As a consequence, we obtain a few corollaries of independent interest: 1) An algorithm to count, sample (and, hence, optimize) over the base polytope of regular matroids when there are additional (succinct) budget constraints and, 2) An algorithm to evaluate and compute mixed characteristic polynomials, that played a central role in the resolution of the Kadison-Singer problem, for certain special cases.

Cite as

L. Elisa Celis, Amit Deshpande, Tarun Kathuria, Damian Straszak, and Nisheeth K. Vishnoi. On the Complexity of Constrained Determinantal Point Processes. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 81, pp. 36:1-36:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)


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@InProceedings{celis_et_al:LIPIcs.APPROX-RANDOM.2017.36,
  author =	{Celis, L. Elisa and Deshpande, Amit and Kathuria, Tarun and Straszak, Damian and Vishnoi, Nisheeth K.},
  title =	{{On the Complexity of Constrained Determinantal Point Processes}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2017)},
  pages =	{36:1--36:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-044-6},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{81},
  editor =	{Jansen, Klaus and Rolim, Jos\'{e} D. P. and Williamson, David P. and Vempala, Santosh S.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX-RANDOM.2017.36},
  URN =		{urn:nbn:de:0030-drops-75851},
  doi =		{10.4230/LIPIcs.APPROX-RANDOM.2017.36},
  annote =	{Keywords: determinantal point processes, constraints, matroids, sampling and counting, polynomials, mixed discriminant}
}
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